LEVEL III SCHWESER’S QuickSheet
Critical Concepts for the 2022 CFA® Exam
SS1: BEHAVIORAL FINANCE
SS2: CAPITAL MARKET
EXPECTATIONS
Cognitive Errors and Emotional Biases
• Cognitive errors—Result from incomplete
information or inability to analyze.
• Emotional biases—Spontaneous reactions that
affect how individuals see information.
Cognitive Errors
• Conservatism bias—Emphasizing information
used in original forecast over new data.
• Confirmation bias—Seeking data to support
beliefs; discounting contradictory facts.
• Representativeness bias—If-then stereotype
heuristic used to classify new information.
ŠŠ Base rate neglect—Too little consideration given
to the initial classification being correct.
ŠŠ Sample size neglect—Inferring too much from a
small new sample of information.
• Control bias—Individuals feel they have more
control over outcomes than they actually have.
• Hindsight bias—Selective memory of past events,
remember correct views and forget errors.
• Anchoring and adjustment—Fixating on a target
number once investor has it in mind.
• Mental accounting bias—Each goal, and
corresponding wealth, is considered separately.
• Framing bias—Viewing information differently
depending on how it is received.
• Availability bias—Future probabilities are
impacted by memorable past events.
Emotional Biases
• Loss aversion bias—Placing more “value” on losses
than on a gain of the same magnitude.
ŠŠ Myopic loss aversion—If individuals systematically
avoid equity to avoid potential short run declines
in value (loss aversion), equity prices will be biased
downward (and future returns biased upward).
• Overconfidence bias—Illusion of having superior
information or ability to interpret.
ŠŠ Prediction overconfidence—Leads to setting
confidence intervals too narrow.
ŠŠ Certainty overconfidence—Overstated
probabilities of success.
• Self-attribution bias—Self-enhancing bias plus selfprotecting bias causes overconfidence.
ŠŠ Self-enhancing bias—Individuals take all the credit
for their successes.
ŠŠ Self-protecting bias—Placing the blame for failure
on someone or something else.
• Self-control bias—Suboptimal savings due to focus
on short-term over long-term goals.
• Status quo bias—Individuals’ tendency to stay in
their current investments.
• Endowment bias—Valuing an asset already held
higher (than if it were not already held).
• Regret-aversion bias—Regret can arise from taking or
not taking action.
ŠŠ Error of commission—From action taken.
ŠŠ Error of omission—From not taking action.
Behavioral biases in DC plan participants:
• Status quo bias—Investors make no changes to
their initial asset allocation.
• Naïve diversification—1/n allocation.
• Disposition effect—Sell winners; hold losers.
• Home bias—Placing a high proportion of assets
in stocks of firms in their own country.
• Mental accounting—See mental accounting bias.
• Gambler’s fallacy—Wrongly predicting reversal
to the mean.
• Social proof bias—Following the beliefs of a
group (i.e., “groupthink”).
Long-term economic growth rate:
pop growth + labor force part. + new cap.
spending + TFP
Taylor rule:
ntarget
= rneutral + iexpected + [0.5(GDPexpected
– GDPtrend) + 0.5(iexpected − itarget)]
= target nominal short-term interest rate
= neutral real short-term interest rate
GDPexpected = expected GDP growth rate
GDPtrend = long-term trend in the GDP growth rate
iexpected
= expected inflation rate
itarget
= target inflation rate
ntarget
rneutral
Risk premium approach to expected bond
return:
risk-free rate + term premium + credit premium
+ liquidity premium
Grinold-Kroner model:
≈ D/P + (%ΔE − %ΔS) + %ΔP/E
= expected equity return
= dividend yield
= percentage change in earnings
= percentage change in shares
outstanding
%ΔP/E = expected repricing return
E(Re)
E(Re)
D/P
%ΔE
%ΔS
Singer-Terhaar model:
Risk premium assuming full integration:
RPi = ρi,Mσi(market Sharpe ratio)
Risk premium assuming full segmentation:
RPi = σi(market Sharpe ratio)
Weighted average risk premium:
RPi = (degree of integration of i) (ERP assuming
full integration) + (degree of segmentation of i)
(ERP assuming full segmentation)
Commercial real estate:
Cap rate = NOI / (property value)
E(Rre) = cap rate + NOI growth rate
For a finite time period: E(Rre) = cap rate +
NOI growth rate – %Δcap rate
MVO use E(R), σ, and correlations to solve
for the efficient frontier (EF) and asset
allocation.
Pitfalls of MVO analysis include: estimating the
inputs, concentrated allocations, and a single
period analysis.
Utility maximization: Um = E(Rm) − 0.005 × λ × Varm
Um
= the investor’s utility from
investing in a portfolio with asset
allocation m
E(Rm)
= the expected return of the
portfolio with asset allocation
m (expressed as a %)
λ
= t he investor’s risk aversion
coefficient (“lambda”)
Varm = σ2m = t he variance of the portfolio with
asset allocation m (expressed as a
%)
• Reverse optimization solves for the E(R)s based
on market weights.
• Black-Litterman view adjusts these returns and
then resolves for an EF.
• Monte Carlo simulation models how an allocation
may perform over time.
SS4: DERIVATIVES AND CURRENCY
MANAGEMENT
Option Strategies
Know the inherent payoff patterns of the option
combinations, then:
• Calculate profit/loss at any ending price for the
underlying as sum of initial investment versus
ending value of the positions held.
• Max gain and loss: examine the payoff pattern
and, from that underlying’s price, sum the initial
investment versus ending value of the positions
held.
• Breakeven(s): examine the payoff pattern and, from
either max gain or loss, determine how much the
underlying must increase or decrease.
Synthetic long forward = long call + short put. Both
options are short the underlying.
• Covered Call
Protective Put
SS3: ASSET ALLOCATION
Asset Allocation Approaches
• Asset-only: focuses on asset return and standard
deviation.
• Liability-relative: focuses on growth of the surplus
and standard deviation.
• Goals-based: uses subportfolios to meet specified
goals.
Asset classes:
• Assets within a class are similar and don’t fit in
more than one class.
• Classes have low correlation to other classes, cover
all investable assets, and are liquid.
Calendar rebalancing is done at a set frequency.
Percentage range rebalancing is when a band
is violated. Wider bands for: higher transaction
cost and correlations between classes, higher risk
tolerance, momentum markets, and less volatile
asset classes.
• Bull Spread
• Bear Spread
Collar: Payoff pattern is
identical to a bull spread
but includes owning the
underlying.
Straddle
• Calendar spread—Options have different
expirations.
• Volatility smile—Further-from-ATM options have
higher implied volatilities resulting in a U-shaped
(smiling) curve when implied volatility is plotted
against strike price.
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DERIVATIVES AND CURRENCY MANAGEMENT continued...
• Volatility skew—Implied volatility increases for
more OTM puts, and decreases for more OTM
calls. Explained by OTM puts being desirable
as insurance against market declines while the
demand for OTM calls is low.
• For an expected increase in equity market volatility
buy an ATM call on volatility index (VIX) futures
and sell an OTM put on VIX futures.
Choosing Options Strategies Based on Direction
and Volatility of the Underlying Asset
Expected
move in
implied
volatility
Decrease
Remain
unchanged
Increase
Outlook on the Trend of Underlying Asset
Bearish
Neutral
Bullish
Write
Write calls
Write puts
straddle
Write calls
Calendar Buy calls and
and buy puts
spread
write puts
Buy puts
Buy straddle Buy calls
Interest rate swaps
Converting fixed-rate and floating-rate exposures:
Existing
Exposure
Floating-rate
liability
Fixed-rate
liability
Floating-rate
asset
Fixed-rate
asset
Converting
Floating to fixed
Fixed to floating
Floating to fixed
Fixed to floating
Interest Rate
Swap Required Beneficial When:
floating rates
Payer swap
expected to rise
floating rates
Receiver swap
expected to fall
floating rates
Receiver swap
expected to fall
floating rates
Payer swap
expected to rise
The notional principal of the interest rate swap.
 MDT − MDP 
(MVP )
NPS = 


MDS
where:
NPS = notional swap principal
MDT = target modified duration
MDP = current portfolio modified duration
MDS = modified duration of swap
MVP = market value of portfolio
Forward rate agreements are typically used to
hedge the uncertainty about a future short-term
borrowing or lending rate.
Hedging Interest Rate Risk Using Treasury
Futures
To hedge the interest rate risk of a long bond portfolio
the fund manager will use Treasury bond futures.
A duration-based hedge ratio (BPV HR) is
calculated to determine the number of futures
contracts required for a hedge.
−BPVportfolio
BPVHR =
× CF
BPVCTD
Basis point value (BPV) is the expected change in
value of a security or portfolio given a one basis
point (0.01%) change in yield.
BPVHR = number of short futures
BPVPortfolio = MDPortfolio × 0.01% × MVPortfolio
MD
= modified duration
BPVCTD = MDCTD × 0.01% × MVCTD
MVCTD = CTD price / 100 × $100,000
To achieve a target duration, the formula can be
amended to:
BPVtarget − BPVportfolio
BPVHR =
× CF
BPVCTD
BPVTarget = MDTarget × 0.0001 × MVPortfolio
Currency forwards and futures allow users to
exchange a specified amount of one currency for a
specified amount of another currency on a future
date. Forwards are customized while futures are
standardized contracts.
The hedge ratio for futures can be calculated as:
HR =
amount of currency to be exchanged
futures contract size
Equity swaps can be used to create a synthetic
exposure to physical stocks, allowing market
participants to increase or decrease their exposure
to equity returns.
The three main types of swaps:
1. Pay fixed, receive equity return
2. Pay floating, receive equity return
3. Pay another equity return, receive equity return
Equity Futures and Forwards
Equity futures are exchange-traded, standardized,
require margin, have low transaction costs, and are
available on indexes and single stocks. They enable
market participants to:
• Implement tactical allocation decisions (alter the
exposure to equity of a portfolio).
ŠŠ Selling futures (short position) reduces equity
exposure.
ŠŠ Buying futures (long position) increases equity
exposure.
• Achieve portfolio diversification.
• Gain exposure to international markets.
• Make directional bets on the direction of the
market.
Forwards provide the same advantages but lack
liquidity, are not subject to mark-to-market margin
adjustments, counterparty credit risk exists, major
advantage is they can be customized.
Achieving a target portfolio beta:
 β − βP  MVP 

number of futures required =  T

 F 
 β
F
where:
βT = target portfolio beta
βP = current portfolio beta
βF = futures beta (beta of stock index)
MVP = market value of portfolio
F
= futures contract value = futures price ×
multiplier
Note that to fully hedge the portfolio from market
risk βT = 0.
VIX Futures
• Negative correlation between the VIX and stock
returns which becomes more pronounced during
equity market downturns.
• An equity holding can be protected from extreme
downturns (tail risk) by buying VIX futures. If
volatility increases the equity portfolio will decline
in value but VIX futures should increase in value.
• VIX futures will increase in value when the
market’s expectation of future volatility at contract
maturity increases.
Position
Long futures position
Short futures position
Long futures position
Short futures position
Term structure
Contango
Contango
Backwardation
Backwardation
Roll yield
Negative
Positive
Positive
Negative
VIX Options
• Call options gain in value if expectations of
volatility at maturity of the option increase.
• Put options gain in value if expectations of
volatility fall.
Variance swaps are based on variance (σ2) rather
than volatility (standard deviation).
Implied variance K2
(fixed at initiation)
Counterparty
1
Counterparty
2
Realized variance σ
(unknown at initiation)
2
There is no initial exchange of notional principal,
no interim settlement periods, and a single
payment at the expiration of the swap based on the
difference between actual and implied variance over
the life of the swap.
Settlement amountT =
(variance notional)(realized variance – variance strike)
Long (purchaser) describes the counterparty who
receives the realized variance (actual) and pays the
swap’s variance strike (implied volatility).
Realized
Buyer (long) of swap
> strike
volatility
makes a profit
Realized
Buyer (long) of swap
< strike
volatility
makes a loss
The notional amount for a variance swap can be
expressed as either variance notional (NVAR) or
vega notional (NVEGA).
vega notional
, so
variance notional =
2 × strike price (K)
profit or loss = NVAR × (σ2 – K2) =
 σ2 − K 2 

N vega ×
 2K 
where:
σ = realized volatility
K = strike volatility (implied volatility)
Both the actual (σ) and the implied volatility (K)
on the swap are quoted in standard deviations, but
remember that this is a variance swap; therefore, we
must square the volatility.
The market convention is to quote the notional
on a swap as vega notional (NVEGA) rather than
variance notional (NVAR). Recall that vega refers to
the change in option premium per a 1% change
∆premium
in volatility,
, a natural way to think
∆volatility
about the return for volatility.
Foreign Currency Equations
RDC = (1 + RFC)(1 + RFX) – 1 = RFC + RFX +
(RFC)(RFX)
RDC ≈ RFC + RFX
RFC = return on the foreign asset and
RFX = return on the foreign currency
σ2(RDC) ≈ σ
2(RFC) + σ2(RFX) + 2σ (RFC) σ(RFX)
ρ(RFC,RFX)
If RFC is a risk-free asset:
σ(RDC) = σ(RFX)(1 + RFC)
Currency Management Strategies
• Passive hedging: eliminates currency risk relative
to the benchmark.
• Discretionary hedging allows the manager to
deviate modestly from passive hedging. The goal
is risk reduction.
• Active currency management allows a manager to
have greater deviations from passive hedging. The
goal is adding value.
• Currency overlay is the outsourcing of currency
management to another manager.
Factors That Shift the Strategic Decision Toward
a Benchmark Neutral or Fully Hedged Strategy
• A short time horizon for portfolio objectives.
• High risk aversion.
• Little weight given to the opportunity costs of
missing positive currency returns.
• High short-term income and liquidity needs.
• Significant foreign currency bond exposure.
• Low hedging costs.
• Clients who doubt the benefits of discretionary
management.
Tactical Currency Management
• Economic fundamentals: in the long term,
relative currency values will converge to their fair
values. Increases in currency values are associated
with currencies:
ŠŠ That are undervalued relative to their
fundamental value.
ŠŠ That have the greatest rate of increase in
fundamental value.
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DERIVATIVES AND CURRENCY MANAGEMENT continued...
ŠŠ With higher real or nominal interest rates.
ŠŠ With lower inflation relative to other countries.
ŠŠ Of countries with decreasing risk premiums.
• Carry trade: borrow in a lower interest rate
currency and invest in a higher interest rate
currency.
• Volatility trading: profit from predicting changes
in currency volatility. If volatility is expected to
increase, purchase an at-the-money call and put
(long straddle). Sell volatility by selling both
options (a short straddle).
Forward Premiums or Discounts and Currency
Hedging Costs
If the hedge requires:
FP/B > SP/B, iB < iP
The forward price
curve is upward
sloping.
A long forward
Negative roll yield,
position in currency B which increases
the hedge earns:
hedging cost and
discourages hedging.
A short forward
Positive roll yield,
position in currency B which decreases
the hedge earns:
hedging cost and
encourages hedging.
FP/B < SP/B, iB > iP
The forward price
curve is downward
sloping.
Positive roll yield,
which decreases
hedging cost and
encourages hedging.
Negative roll yield,
which increases
hedging cost and
discourages.
The minimum-variance hedge ratio (MVHR): a
regression of past changes in value of the portfolio
to past changes in value of the foreign currency.
The hedge ratio is the beta (slope coefficient) of
that regression.
• Strong positive correlation between RFX and RFC
increases the volatility of RDC resulting in a hedge
ratio > 1.0.
• Strong negative correlation between RFX and RFC
decreases the volatility of RDC resulting in a hedge
ratio < 1.0.
SS5 & 6: FIXED INCOME
Liability-based mandates:
• Cash flow matching directly funds liabilities with
coupon and par amounts.
• Duration matching requires:
• PVA = PVL; there are exceptions when asset
and liability discount rates differ.
• DA = DL or BPVA = BPVL
• Minimize portfolio convexity but make it
greater than that of the liabilities.
• Derivatives overlays:
• involving the use of futures or swaps
contracts, can be used to implement duration
matching or contingent immunization
strategies.
Regularly rebalance the portfolio:
ŠŠ BPVfutures ≈ BPVCTD / CFCTD
ŠŠ BPV = MD × V × 0.0001
ŠŠ Nf = (BPVL – current BPV) / BPVfutures
• Nonparallel yield curve shifts can be
a problem, match key rate durations:
%Δ value = –MDkey rate n Δyn
• Contingent immunization: active management
if the surplus is positive.
(PV− ) − (PV+ )
Effective duration =
2(∆Curve)(PV0 )
Effective convexity =
(PV− ) + (PV+ ) − 2(PV0 )
(∆Curve)2 (PV0 )
where:
PV0 = current value of the portfolio
PV– = value of portfolio when benchmark curve
is shifted down
PV+ = value of portfolio when benchmark curve
is shifted up
ΔCurve = change in benchmark curve
Return can be projected (or actual return
decomposed) as the sum of:
1. Coupon income: annual coupon amount /
current bond price
2. Rolldown return, assuming no change in yield
curve: (projected ending bond price (BP) −
beginning BP) / beginning BP
3. Price change due to investor yield change
predictions: (–MD × ΔY) + (½C × ΔY2)
4. Price change due to investor yield change
predictions: (–MD × ΔS) + (½C × ΔS2)
5. Currency G/L: projected change in value of foreign
currencies weighted for exposure to the currency
Coupon income + rolldown return may be referred
to as rolling yield.
Leveraged return = rI + [(VB / VE) × (rI – rB)].
where:
rp = return on portfolio
rI = return on invested assets
rB = rate paid on borrowings
VB = amount of leverage
VE = amount of equity invested
Active management for a stable upward sloping
yield curve:
• Buy and hold: extend duration to get higher yields.
• Roll down the yield curve: portfolio weighting
highest for securities at the long end of the
steepest yield curve segments, maximize gains
on securities from declines in yield as time
passes.
• Repo carry trade: borrow at lower rates to
purchase securities with higher rates.
• Long futures position
• Receive-fixed swap
Active management for a changing yield curve:
• Increase (decrease) portfolio duration if rates are
expected to decrease (increase).
• Add call options on either a bond price or a
bond futures contract to increase duration and
convexity.
• Add put options on either a bond price or
bond futures contract to decrease duration and
convexity.
• A payer swaption (right to enter a pay-fixed swap
decreases duration and convexity.
• A receiver swaption (right to enter a receive-fixed
swap) increases duration and convexity.
KeyRateDur = −
change in portfolio value
portfolio value × change in key rate
• Increase portfolio convexity (decreasing yield)
when large changes in rates are expected.
• Bullet portfolios have more yield, but barbells
have more convexity and also tend to outperform
in curve-flattening environments.
Curvature of the yield curve can be measured
through the butterfly spread: butterfly spread =
–(short-term yield) + (2 × medium-term yield) –
long-term yield
• % Δ value = –MDΔy
• %Δrelative value = –SDΔs where spread duration
(SD) measures a portfolio’s percentage sensitivity
to a 1% change in credit spreads (Δs).
• spread = yhigher yield – ygovernment
• spread ≈ POD × LGD
(PV− ) − (PV+ )
• EffRateDurFRN =
2( ∆ MRR )(PV0 )
(PV− ) − (PV+ )
2(∆DM)(PV0 )
(PV− ) − (PV+ )
• effective spread duration =
2(∆spread )(PV0 )
• EffSpreadDurFRN =
• effective spread convexity =
(PV− ) + (PV+ ) − 2(PV0 )
(∆spread )2 (PV0 )
• %Δprice = (–EffSpreadDur × Δspread) +
(½ × EffSpreadCon × Δspread2)
• Expected excess spread = spread – (EffSpreadDur
× Δspread) – (POD × LGD)
• Effective spread for a buy order = trade size ×
(trade price – midquote)
• Effective spread for a sell order = trade size ×
(midquote – trade price) where: midquote = (bid
+ ask) / 2
• CDS price ≈ 1 + [(fixed coupon – CDS spread) ×
EffSpreadDurCDS]
SS7 & 8: EQUITIES
Constructing and maintaining the index involves:
• The weighting method to construct the index:
(1) market-cap weighting, (2) price weighting,
(3) equal weighting, or (4) fundamental weighting.
• Considering the level of stock concentration. The
“effective number of stocks” can be determined as the
reciprocal of the Herfindahl-Hirschman index (HHI):
n
HHI =
∑ w2i
i =1
1
HHI
Common equity risk factors: growth, value, size,
yield, momentum, quality, and volatility.
Factor-based strategies: return oriented, risk
oriented, and diversification oriented.
Common approaches to passive equity investing
use: (1) pooled investments, such as open-end mutual
funds and ETFs, (2) derivatives-based strategies, and
(3) separately-managed index-based portfolios.
Three methods of constructing passively managed
index-based equity portfolios: (1) full replication,
(2) stratified sampling, often based on cell matching,
(3) technical and quantitative approach (optimization)
Fundamental managers use discretionary judgment
vs. quantitative managers use rules-based
(systematic) data-driven models.
Fundamental law of active management:
effective number of stocks =
E(R A ) = IC BR σRA TC
Active share measures the degree to which the number
and sizing of the positions in a manager’s portfolio
differ to those of a benchmark:
n
1
Active share =
Wp,i − Wb,i
2
∑
i=1
Active risk (tracking error), is the standard
deviation of active returns (portfolio returns minus
benchmark returns).
Long extension portfolios guarantee investors
100% net exposure with a specified short exposure.
A typical 130/30 fund will have 130% long and
30% short positions.
Market-neutral portfolios aim to remove market
exposure through offsetting long and short positions.
Pairs trading is a common technique in building
market-neutral portfolios, with quantitative pair
trading referred to as statistical arbitrage.
Benefits of long/short strategies include the ability
to better express negative views, the ability to gear
into high-conviction long positions, the removal
of market risk to diversify, and the ability to better
control risk factor exposures.
Drawbacks of long/short strategies include potential
large losses since share prices are not bounded above,
negative exposures to risk premiums, potentially
high leverage for market-neutral funds, and the costs
of borrowing securities and collateral demands from
prime brokers. Being subject to a short squeeze on
short positions is also a risk.
SS9: ALTERNATIVE INVESTMENTS
Hedge Funds Strategies:
1. Equity related with the primary source of risk
being equity risk.
a. Long/short equity—The fund manager takes
long positions in stocks that they think will
rise in value, and takes short positions in stocks
that they believe will fall in value.
b. Dedicated short bias funds—These seek
overpriced securities to sell short.
c. Equity market neutral—These seek to attain a
near-zero overall exposure to the stock market.
ŠŠ Take long positions in undervalued stocks
and short positions in overvalued stocks with
the betas of the positions summing to zero.
ŠŠ Alpha occurs through mean reversion.
2. Event-driven relate to corporate actions such
as governance activities, mergers, acquisitions,
bankruptcies, and other major business events.
The main risk is event risk.
a. Merger arbitrage earns a return from the
uncertainty that exists in the market from when
an acquisition is announced until completed
(i.e., the fund manager purchases the stock of
the target company and shorts the stock of the
acquiring company, anticipating the deal will
be completed).
b. Distressed securities take positions in the
securities of firms that are in financial distress,
including firms that are in bankruptcy or nearbankruptcy.
3. Relative value strategies profit from the relative
valuation differences between securities.
a. Fixed-income arbitrage takes advantage
of temporary mispricing of fixed-income
instruments by going long undervalued
securities and short overvalued securities.
ŠŠ Yield curve trades go long and short fixedincome investments in order to profit from
the anticipated yield curve steepening or
flattening.
ŠŠ Carry trade the portfolio manager shorts a
low-yielding security and goes long a highyielding security.
b. Convertible bond arbitrage the manager purchases
the convertible bond which is often underpriced
and short sells the underlying equity.
4. Opportunistic strategies employ a topdown approach making macro investments on
a global basis across regions, sectors, and asset
classes.
a. Global macro profits from making correct
assessments and forecasts of various global
economic variables.
b. Managed futures strategies take long and short
positions in derivatives contracts.
5. Specialist strategies require specialized market
expertise or knowledge.
a. Volatility strategies trade volatility-related assets
globally.
b. Insurance/reinsurance strategies:
ŠŠ Insurance strategy—An insured person sells
their insurance policy (through a broker) to
a hedge fund.
ŠŠ Reinsurance strategies—Insurance companies
sell off some of their risk to reinsurance
companies who may then sell the risk to
hedge funds in exchange for capital.
6. Multimanager strategies use other hedge fund
strategies as building blocks, combining different
strategies together, rebalancing exposures over
time.
Drawdown:
• Defined as the percentage peak-to-trough decline
for a portfolio.
• High-water mark refers to the maximum value the
portfolio has ever reached.
Estimating investor cash flows to and from a
private investment:
• Capital contribution in period t = percentage
to be called in period t × (committed capital –
capital previously called)
• Distributions in period t = percentage to be
distributed in period t × [NAV in period t – 1 ×
(1 + growth rate)]
• NAV in period t = [NAV in period t – 1 ×
(1 + growth rate)] + contributions in period t –
distributions in period t
SS10 & 11: PRIVATE WEALTH
OVERVIEW OF PRIVATE WEALTH
MANAGEMENT
Behavioral Biases Associated with Retirees:
• Increased loss aversion. Affects return assumptions
and asset allocation decisions in retirement.
• Consumption gaps. Consumption spending tends
to be lower than what economic studies forecast,
can be attributed to loss aversion and uncertainty
about future retirement spending.
• The “annuity puzzle”. Individuals tend to
avoid buying annuities, possible explanations
include: (a) clinging to hope of funding a
better retirement lifestyle, (b) a desire to keep
control of assets, and (c) the high cost of annuities.
• Mental accounting and lack of self-control. Retirees
prefer to meet their spending needs from investment
income rather than liquidating securities.
IPS for a Private Clients:
• Client Background obtained from relevant
personal, financial and tax information. Investment
Objectives may be planned, unplanned, ongoing,
or one-off. Multiple objectives should be prioritized
into primary and secondary objectives.
• Key Investment Parameters:
ŠŠ Risk tolerance—willingness and ability, low risk
tolerance usually associated with high priority
goals and near-term goals.
ŠŠ Time horizon—described as a range (e.g. in excess
of 15 years for a long horizon and less than 10
years for a short horizon). If multiple objectives, a
different time horizon for each objective.
ŠŠ Other investment parameters—include asset class
preferences, liquidity preferences (including a cash
reserve), unique investment preferences.
ŠŠ Constraints—restricting investments for client’s
portfolio.
• Asset Allocation—Strategic long-term target
asset allocation for each asset class and tactical
asset allocation as an active management strategy
specifying a range for each asset class.
• Portfolio Management and Implementation
guidelines for discretionary authority, portfolio
rebalancing, tactical asset allocation changes, and
acceptable investment vehicles.
• Wealth Manager Duties and Responsibilities
include; formulating/reviewing the client’s IPS,
constructing the portfolio, monitoring and
rebalancing the portfolio, monitoring portfolio
costs and third-party providers, and reporting
portfolio performance.
• IPS Appendix includes modelled portfolio
performance and capital market expectations.
Portfolio Construction:
• Traditional Approach—views risk in an overall
portfolio context.
• Goals-based investing—separate portfolios are
created for each of the client’s goals. Mean-variance
optimization used to maximize expected returns
for a given level of risk or to meet a specified
probability of success is carried out for each goal
portfolio rather than for the entire portfolio.
TOPICS IN PRIVATE WEALTH
MANAGEMENT
• Main categories of taxes: income tax, capital gains
tax, wealth/property tax, stamp duties, wealth
transfer tax.
• General equation for capital gains: net sales price –
tax (cost) basis = capital gain/loss.
• Three main types of investment accounts: taxable,
tax-deferred (TDA), and tax-exempt (TEA).
Common metrics used in examining tax efficiency:
1. After-tax holding period return R' =
[(value1 – value0) + income – tax] / value0
Alternatively, R' = R – (tax / value0).
2. After-tax post-liquidation return (RPL) involves
deducting the implied tax:
RPL = [(1 + R'1)(1 + R'2)…(1 + R'n) – (liquidation
tax/final value)]1/n – 1. Liquidation tax = (final
value – tax basis) × tax rate on capital gains
3. After-tax excess return (x') is computed as the
after-tax return of the portfolio (R') minus the
after-tax return of the benchmark (B'):
x' = R' – B'. In this regard, the tax alpha would
be defined as after-tax excess return (x') minus the
pretax excess return (x): atax = x' – x
4. Tax-efficiency ratio (TER) is calculated as after-tax
return (R') divided by pretax return (R):TER = R' / R
Taxable accounts involve one or more tax rates on
income (e.g., interest, dividends) or return (e.g.,
realized capital gains) to determine R’: FVAT = (1 + R’)n
Tax exempt accounts (TEAs), after-tax funds are
deposited so no tax is due on the returns earned or
on withdrawals: FVAT = (1 + R)n
Tax deferred accounts (TDAs), pretax funds
are deposited and the investor may take a tax
deduction for the amount contributed thereby
reducing taxable income and taxes due. All tax is
deferred until withdrawal allowing tax-deferred
compounding: FVAT = (1 + R)n(1 – t)
Tax-efficient assets (e.g., equities that generate capital
gains are often subject to lower tax rates) should be
placed in taxable accounts. Tax-inefficient assets
(e.g., taxable bonds that generate taxable interest,
which is often subject to higher tax rates) should be
placed in tax-exempt or tax-deferred accounts.
Four common investment vehicles include:
• Partnership
• Mutual fund
• Exchange-traded fund (ETF)
• Separately managed account (SMA)
Tax loss harvesting involves the sale of securities
with embedded losses to offset gains, which will
lower the tax liability for the current year.
• Highest in, first out (HIFO) is generally optimal
• In case future tax rates are expected to be higher
than current tax rates, first in, first out (FIFO)
may be better
• In case future tax rates are expected to be lower than
current tax rates, last in, first out (LIFO) may be better
Strategies for managing a concentrated position in
public equities:
• Staged diversification strategy over multiple years
to spread out tax liability
• Completion portfolio using other assets to
complement/complete the concentrated position
• Equity monetization by hedging a large part of
the risk in the position using derivatives and then
borrow using the hedged position as collateral
• Zero-cost collars are used to lower initial cost by
giving up some stock upside. The put premium
paid and call premium received are equal.
• Covered call writing is possibly a staged
diversification assuming the share price
appreciates sufficiently
• Exchange fund with a pooling of investments on
a tax-free basis
continued on next page...
PRIVATE WEALTH continued...
• Charitable remainder trust to benefit both
beneficiaries and a designated charity
Strategies for managing concentrated positions in
privately owned businesses:
• IPO
• Direct sale to another investor
• Sale of non-essential business assets
• Personal line of credit secured by company shares
(owner borrows from company or from a thirdparty lender)
• Leveraged recapitalization (e.g., private equity firm)
• Sale to employee stock ownership plan
SS12: INSTITUTIONAL INVESTORS
Stakeholders and key elements of the IPS for
defined benefit (DB) pension plans vs. defined
contribution (DC) pension plans:
Stakeholders
Liabilities
Lifetime Gifts vs. Testamentary Bequests
Basic form of the relative value (RV) ratio: FV
after-tax to the receiver if gifted now / FV after-tax
to the receiver if bequested at death:
Two tax scenarios to consider:
• The gift now is tax free to both the receiver and
the donor
• The gift is taxable with tax paid by the receiver
Relevant tax factors to consider:
• rg and tg are the pretax return earned and the
applicable tax rate on those earnings for assets
held by the gift receiver
• re and te are the pretax return earned and the
applicable tax rate on those earnings for assets
held by the gift giver
• Te is the estate tax rate and would be paid from
the estate
• Tg is the gift tax rate and is assumed to be paid
by the receiver
FVgift = [1 + rg(1 – tg)]n FVbequest
= [1 + re(1 – te)]n(1 – Te)
• RV of a tax-free gift, Tg = 0
n
• RVTax Free Gift =
Liquidity
needs
External
constraints
1 + r 1 − t 
g(
g )
FVGift

=
FVBequest
1 + re (1 − t e ) n (1 − Te )


• RV of a taxable gift, Tg paid by receiver
• RVTaxable Gift =
Investment
time horizon
n
1 + r 1 − t
g(
g ) (1 − Tg )
FVGift

=
FVBequest
1 + re (1 − t e ) n (1 − Te )


RISK MANAGEMENT FOR I­ NDIVIDUALS
• Total wealth is composed of both human capital
(HC) and financial capital (FC). HC is the
discounted present value of expected future labor
income. FC is the sum of all the other assets of an
individual.
• Net wealth is the sum of the individual’s
FC and HC less any liabilities owed by the
individual.
• The economic (holistic) balance sheet
extends the traditional balance sheet assets
to include HC. Liabilities can also be
extended to include consumption and bequest
goals.
• Earnings risk: Use disability income insurance.
• Premature death risk: Use life insurance.
• Longevity risk of living too long: Use annuities.
• Property risk: Loss in value of physical property
(FC). Use property insurance (homeowner’s and
automobile).
• Liability risk: If legally responsible for damages.
Use liability insurance.
• Health risk: Direct loss of FC to pay illness or
injury related expenses and may reduce HC. Use
health and medical insurance.
Asset allocation based on investor’s total economic
wealth, FC and HC:
• Individual employed in a high risk profession
would choose lower risk FC.
• If HC is positively correlated with the stock
market then best to select asset classes other than
equity for risky assets used.
• Avoid FC tied directly to employer.
Investment
objectives
DB Plan
Employers, plan
beneficiaries,
investment staff,
investment committee/
board, governments,
shareholders
Present value of future
benefits promised to
plan participants. Higher
when:
• Employees work
longer
• Salaries are higher
• Participants live
longer
• Lower employee
turnover leads to
higher vesting
• Discount rate is low
Longer if proportion of
active lives is higher
Higher with:
• More retired lives
• Older workforce
• Higher funded
status (may reduce
contributions)
• Flexibility of
participants to switch
plans
• Regulations vary by
country: IORP II
in Europe, ERISA
in U.S.
• Tax treatment
favorable
• Accounting rules: ASC
715 requires funded
status to be shown
on balance sheet
(U.S. GAAP); public
pension plans follow
GASB
Achieve a long-term
target return over a
specified horizon with
appropriate risk to meet
contractual liabilities.
DC Plan
Employers, plan
beneficiaries,
investment staff,
investment committee/
board, governments
No liability to plan
sponsor once required
contribution to plan has
been met
Dependent on the age
of participant: longer if
younger
Higher with:
• Older workforce
• Flexibility of
participants to switch
plans
• Regulations vary by
country: IORP II
in Europe, ERISA
in U.S.
• Sponsor must offer
appropriate default
option to disengaged
participants
• Plans are tax deferred
Prudently grow assets to
meet spending needs in
retirement.
Stakeholders and key elements of the IPS for
university endowments and private foundations:
University Endowments
Private Foundations
Stakeholders Current and future
Founding family, donors,
students, alumni,
grant recipients and
university employees
broader community,
governments
Liabilities
Set by the future
U.S. tax rules require
spending promised to the minimum spending
university.
of 5% of assets plus
Spending policy should investment expenses.
consider (1) ongoing
Must also spend
donations, (2) reliance
donations in the same
of university on
year they are received.
spending, (3) ability to
issue debt. Spending
may use a spending rule
which takes a weighted
average of last period’s
spending adjusted for
inflation and a fixed
spending rate applied to
average AUM.
Investment Perpetual
Typically perpetual, but
time horizon
shortened for limited-life
foundations
Liquidity
The spending rate net of Higher than
needs
donations is very low at endowments—legally
2%–4% of assets.
required to spend 5%
of assets. Reliance
on spending by
foundation is usually
higher than the
reliance of a university
on endowment
spending.
External
Typically tax exempt. Regulation varies by
constraints jurisdiction but generally requires a total return
approach and prudence in investing (UPMIFA in
U.S., The Trustee Act in the U.K.).
Investment Generate a total real
Generate a real return
objectives
return after inflation
over consumer price
measure by the HEPI
inflation of the spending
of about 5% on a
rate (minimum 5%) plus
3–5 year rolling basis,
investment expenses on
with reasonable annual a 3–5 year rolling basis,
volatility in the range of with reasonable annual
10%–15%
volatility in the range of
10%–15%
Stakeholders and key elements of the IPS for banks
and insurers:
Stakeholders
Stakeholders and key elements of the IPS for the
five types of sovereign wealth funds (SWF):
Budget
Stabiliza- DevelopPension
tion
ment
Savings Reserve
Reserve
StakeCountry’s citizens, the government, external and interholders nal investment management
Liabilities Uncertain: Linked to Spending Yield
Future
linked to socio-eco- on future prompension
commod- nomic
genera- ised on Payments
ity prices/ investtions
central
economic ments
bank/
cycle
government
bonds
InvestShort term Long/me- Long
Long
Long
ment
dium term term
term
term
time
dependent
horizon
on investment
projects
Liquidity Highest
Generally Lowest Interme- Varies: low
needs
low
diate
during
accumulation stage,
higher
during
decumulation stage
External Established by national legislation. Best practice set by
conISWF’s Santiago Principles.
straints Generally tax exempt.
InvestCapital
Real
Maintain Grow
Earn
ment ob- preserva- growth
real
faster
returns
jectives tion
higher
perpetual than
to meet
than real spending yield on future
GDP
central unfunded
growth
bank/
governgovern- ment
ment
pension
bonds
payments
Liabilities
Investment
time horizon
Liquidity
needs
External
constraints
Investment
objectives
Banks
External: shareholder,
depositors, borrowers,
creditors, credit
ratings agencies,
regulators, and
communities
Internal: employees,
management, and
board
Primarily deposits
which are short term
Insurers
External: shareholders,
policyholders, derivatives
counterparties, creditors,
regulators, credit ratings
agencies
Internal: employees,
management, and board
Life insurers: long
duration contract
payouts
P&C insurers: shorter
and less certain contract
payouts
While perpetual organizations, investments are
run on a short/medium term LDI basis.
Driven by deposit
Varies by product
withdrawals and
line—P&C liquidity
potential need to raise needs generally higher
liquidity in adverse
than life. Liquidity
market conditions.
needs will increase
Regulators apply
in times of high
liquidity coverage ratios interest rates due
and net stable funding to policyholders
ratios.
surrendering in
search of high yields
elsewhere.
Highly regulated due to importance to real
economy and systemic risk, particularly
SIFIs. Main goal of regulators is to ensure the
institution holds sufficient risk-based capital to
absorb losses.
Three different types of accounting systems apply:
1. Standard financial reporting (GAAP or IFRS)
2. Statutory accounting for regulators (more
conservative than financial reporting)
3. True economic accounting (marked-tomarket)
Banks and insurers are fully taxable.
Manage liquidity and risk mismatches between
the institution’s non-investment assets and
liabilities. This needs to be done in the context
of the institution’s overall profit maximization
objective.
SS13: TRADING, PERFORMANCE
EVALUATION, AND MANAGER
SELECTION
Implementation shortfall (IS) at the highest level
the absolute value is:
IS = paper return – actual return
IS can be decomposed into the following parts:
• Execution cost occurs due to executing shares at
a less favorable price than the original decision
price. Execution cost can be further broken
down into:
ŠŠ Delay cost occurs due to adverse price movements
in the time between the portfolio manager
submits the order to the trader and the time the
trader releases the order to the market. For a buy
order: delay cost = shares executed × (arrival
price – decision price)
ŠŠ Decision price = price when manager decides
to buy (or sell).
ŠŠ Arrival price = price when the order is placed
by trader.
ŠŠ Trading cost: due to the market impact of
executing the trade.
Trading cost = shares executed × (average purchase
price – arrival price)
• Opportunity cost is the cost of not trading any
unfilled part of the order. The paper portfolio
assumes that all shares are executed immediately at
the original decision price. The actual trade may
have only filled part of the order and the lost profit
on the unfilled portion is the opportunity cost. For
a buy order:
Opportunity cost = portion of order not filled ×
(closing price – decision price)
• Fixed fees are any explicit commissions or fees
incurred in executing the trade.
Fixed fees = shares executed × commission per share
Total IS value ($) = delay cost + trading cost +
opportunity cost + fixed fees
All of the components of and total IS can be expressed
in terms of basis points (bps) of the original cost of the
paper portfolio. A basis point is 1/100th of one percent.
A decimal number is multiplied by 10,000 to convert
it to basis points.
Trade costs represent costs relative to the
benchmark, a positive value represents
underperformance:
Absolute cost ($) = side × (execution price –
benchmark price) × shares executed
Trade cost (bps) =
side ×
(execution price − benchmark price)
benchmark price
×10, 000
where:
side = +1 for a buy order, –1 for a sell order
Market-adjusted cost is used to remove the impact
of market movements on trade cost which ensures
a trader is not penalized or rewarded for general
market movements over the trade horizon.
index cost (bps) =
(index VWAP − index arrival price)
side ×
×100, 000
index arrival price
Market-adjusted cost (bps) = arrival cost (bps) – β ×
index cost (bps)
where:
arrival cost is the arrival cost of the trade based on
an arrival price benchmark
β = beta of the security vs. the index used to
calculate index cost
Added value is a different method of trade cost
analysis comparing the arrival cost of the trade with
the estimated pre-trade cost.
Added value (bps) = arrival cost (bps) – estimated
pre-trade cost (bps)
A negative cost is a benefit—the trader has added
value through their trading decisions.
Micro Attribution vs. Macro Attribution
• Micro attribution analyzes the portfolio at the
portfolio manager’s level.
• Macro attribution analyzes investment decisions at
the fund sponsor’s level.
Returns-Based, Holdings-Based, and
Transactions-Based Attribution
• Returns-based attribution uses regressions to analyze
the portfolio returns over time and isolates the
asset class components through indices that would
have generated these returns.
• Holdings-based attribution uses beginning-of-period
portfolio assets.
• Transactions-based attribution updates the
beginning-of-period holdings-based attribution for
any subsequent trades.
Brinson-Fachler and Brinson, Hood,
Beebower (BHB) models quantify the portfolio
returns into three attribution effects: allocation
effect, security selection effect, and the
interaction effect.
• Allocation effect refers to the portfolio
manager’s decision to overweight or underweight
specific sector weightings versus the benchmark.
Using the Brinson-Fachler model, the
contribution to the ith sector is equal to the
portfolio’s sector weight minus the benchmark’s
sector weight, times the benchmark sector
return minus the overall benchmark return:
Ai = (wi – Wi)(Bi – B). For the BHB model, the
contribution to the ith sector is equal to the
portfolio’s sector weight minus the benchmark’s
sector weight, times the benchmark sector return:
Ai = (wi – Wi)Bi
• Security selection is the portfolio manager’s
value added by selecting individual securities
(stock picking) within the sector and weighting
the portfolio differently compared to the
benchmark’s weightings. The contribution
to selection in the ith sector is equal to the
benchmark sec­tor weight times the portfolio’s
sector return minus the benchmark’s sector
return: Si = Wi(Ri – Bi)
• Interaction effect is a residual amount (e.g., plug)
that ensures the arithmetic return minus the
relative benchmark is fully accounted for in
attribution analysis. The contribution to the ith
sector is equal to the portfolio sector weight minus
the benchmark sector weight, times the portfolio
sector return minus the benchmark sector return:
Ii = (wi – Wi)(Ri – Bi)
Carhart model is a fundamental factor model
calculating the excess return from active
management decisions by determining the impact
on the portfolio due to the following factors:
(1) market index (RMRF), (2) market-capitalization
(SMB), (3) book-value-to-price (HML), and (4)
momentum (WML):
Rp – Rf = ap + bp1RMRF + bp2SMB + bp3HML +
bp4WML + Ep
Benchmark quality of a portfolio return can be
broken up into three components: market, style,
and active management.
P=M+S+A
where:
P = investment manager’s portfolio return
M = return on the market index
S = B − M = excess return to style; difference
between the manager’s style index
(benchmark) return and the market return
(S can be positive or negative)
A = P − B = active return; difference between
the manager’s overall portfolio return and
the style benchmark return
Performance Appraisal
Sharpe ratio
SA =
R A − rf
σA
Treynor ratio
TA =
R A − rf
βA
Information ratio is used to measure a portfolio’s
performance against the benchmark accounting for
differences in risk.
IR =
E (rp ) − E (rB )
σ (rp − rB )
Appraisal ratio is calculated as alpha divided by the
standard deviation of the residual/unsystematic risk
(the standard error of regression).
α
AR =
σε
Sortino ratio only considers the standard deviation
of the downside risk where rT refers to the
minimum acceptable return (MAR) and (σD) refers
to target semistandard deviation.
SR D =
E (rp ) − rt
σD
Capture ratios determine the manager’s relative
performance when markets are up or down.
Capture is calculated as portfolio return divided by
benchmark return. The capture ratio is calculated
as upside capture divided by downside capture.
Type I and II errors in hiring managers and
continuation decisions
• Null hypothesis (H0) is that there is no value
added.
• Type I error is when the null hypothesis is rejected
when in fact there was no value added.
• Type II error is when the null hypothesis is not
rejected when in fact there was value added.
SS14: CASES IN PORTFOLIO
MANAGEMENT AND RISK
MANAGEMENT
• Review the SchweserNotesTM and/or the
SchweserNotes Videos.
SS15 & 16: ETHICS (INCLUDING GIPS)
ISBN: 978-1-0788-1807-0
9 781078 818070
Revised July 2021
© 2021 Kaplan, Inc. All Rights Reserved.
Review the SchweserNotesTM and/or SchweserNotes
Videos and questions in the SchweserNotes™,
CFA® text, and SchweserPro™.